A 9-digit palindrome has the structure where the first five digits determine the last four digits in reverse order. The first digit must be from 1 to 9 (to ensure it's a 9-digit number), giving us 9 options. The next four digits (the second to fifth digits) can each be any digit from 0 to 9, providing 10 options each. Therefore, the total number of 9-digit palindromes is (9 \times 10^4 = 90,000).
9 of them.
There are 199 palindromic numbers between 0 and 1000. These include single-digit numbers (0 to 9), two-digit numbers (e.g., 11, 22, ... 99), and three-digit numbers (e.g., 101, 111, ... 999). Each of these categories contributes to the total, with the three-digit palindromes being in the form of ABA, where A and B are digits.
Between 900 and 1900, the palindromes are numbers that read the same forwards and backwards. These are specifically the three-digit numbers in the form of "aba," where "a" is a digit from 9 to 1, and "b" is any digit from 0 to 9. The palindromes in this range are: 909, 919, 929, 939, 949, 959, 969, 979, 989, 999, 1001, 1111, 1221, 1331, 1441, 1551, 1661, 1771, 1881, and 1991. In total, there are 19 palindromes between 900 and 1900.
Nine. The sum of the digits must be a multiple of 9; because of the repeated digits, this is only possible if the first two digits add up to 9.
-900
-1000
9 of them.
-4
There are 199 palindromic numbers between 0 and 1000. These include single-digit numbers (0 to 9), two-digit numbers (e.g., 11, 22, ... 99), and three-digit numbers (e.g., 101, 111, ... 999). Each of these categories contributes to the total, with the three-digit palindromes being in the form of ABA, where A and B are digits.
Between 900 and 1900, the palindromes are numbers that read the same forwards and backwards. These are specifically the three-digit numbers in the form of "aba," where "a" is a digit from 9 to 1, and "b" is any digit from 0 to 9. The palindromes in this range are: 909, 919, 929, 939, 949, 959, 969, 979, 989, 999, 1001, 1111, 1221, 1331, 1441, 1551, 1661, 1771, 1881, and 1991. In total, there are 19 palindromes between 900 and 1900.
Nine. The sum of the digits must be a multiple of 9; because of the repeated digits, this is only possible if the first two digits add up to 9.
-900
There are 90 palindromes with 4 digits.The first digit can be any digit from the set {1,2,3,4,5,6,7,8,9}.With each choice of the first digit, the second can be any digit from the set {0,1,2,3,4,5,6,7,8,9}.That makes 9*10 = 90 permutations for the first two digits. These determine the palindrome since the third and fourth digits are the same as the second and first, respectively.
There are more 12-digit palindromic numbers than 11-digit palindromic numbers. This is because the number of possible 12-digit palindromic numbers is greater than the number of possible 11-digit palindromic numbers. In general, the number of palindromic numbers of length n is 9 * 10^((n-1)/2), so for 11-digit palindromic numbers, there are 9 * 10^5 = 900,000 possibilities, while for 12-digit palindromic numbers, there are 9 * 10^6 = 9,000,000 possibilities.
There are 9,000 palindromes between 10,000 and 99,999. A five-digit palindrome takes the form (abcba), where (a) can range from 1 to 9 (9 options), and (b) and (c) can each range from 0 to 9 (10 options each). Thus, the total number of five-digit palindromes is (9 \times 10 \times 10 = 9000).
No, 100 different digits cannot make 10,010,010,000 different three-digit palindromes. A three-digit palindrome has the form "ABA," where A is the first and last digit, and B is the middle digit. Since A can be any digit from 1 to 9 (for the first digit) and B can be any digit from 0 to 9, there are only 9 options for A and 10 options for B, resulting in a total of 90 unique three-digit palindromes (9 x 10 = 90).
Yes, a single digit is considered a palindrome because it reads the same forwards and backwards. For example, the digit "5" is the same in both directions. All single-digit numbers (0-9) are palindromes by this definition.